"I have learned a lot during my time both in and out of Senate leadership. During my two terms as NSC Chair, we shrunk Democrats' majority by five seats and laid the foundation to retake the majority in 2014. Then as the Republican Whip, I helped President Trump advance his agenda through the Senate, including passing historic tax reform and remaking our judiciary - including two Supreme Court Justices," he said.

"Throughout my time I've built a track record of listening to colleagues and seeking consensus, while leading the fight to stop bad policies that are harmful to our nation and the conservative cause. I believe the Senate is broken - that is not news to anyone. The good news is that it can be fixed, and I intend to play a major role in fixing it," he added.

Cornyn said he is "confident Senate Republicans can restore our institution to the essential role it serves in our constitutional republic."